Question

noah clue’s work for the following algebra problem is given below:
when the foresthill wildfire band returned from a recent competition, 24 of the students attended school before realizing they had contracted a strong flu virus. the virus quickly spread and each day the number of students with the flu increased by an estimated 30%. how many people will have the flu after five days?
\\( y = 24(0.3)^5 \\)
\\( y = 0.0582 \\)
explain completely what noah’s mistake is
and write a complete solution to the problem.

Explanation:

Step1: Identify Noah's error

Noah used the growth factor incorrectly. For a 30% daily increase, the growth factor is $1 + 0.3 = 1.3$, not $0.3$. The formula he used represents decay, not growth.

Step2: State correct growth formula

The exponential growth formula is $y = a(1 + r)^t$, where $a=24$ (initial number), $r=0.3$ (daily growth rate), $t=5$ (days).

Step3: Substitute values into formula

$y = 24(1 + 0.3)^5 = 24(1.3)^5$

Step4: Calculate $(1.3)^5$

$1.3^5 = 1.3\times1.3\times1.3\times1.3\times1.3 = 3.71293$

Step5: Compute final number

$y = 24\times3.71293$

Answer:

Noah's mistake was using the decimal form of the growth rate ($0.3$) as the growth factor instead of the correct growth factor of $1.3$ (which accounts for the original number of infected students plus the 30% increase).

The correct number of students with the flu after 5 days is $\boldsymbol{89.11032}$, which we round to 89 students (since we cannot have a fraction of a student).